Chromatography Forum

Rather than compare the signal to noise, I have been asked to make a meaningful comparison between the ratio of two baseline corrected peak areas and the peak-to-peak noise. Can this be done?

You need to talk to your advisor/professor and get some background on what question is being asked (or, what hypothesis is being tested!). Here's a *possible* interpretation:

In principle, if you take the ratio of two quantities that are subject to errors (expressed as relative standard deviation):
- if the errors are perfectly correlated, they will cancel and the ratio will be error-free (in practice, nothing is perfectly correlated, but the relative standard deviation of the ratio will be lower than the relative standard deviations of the individual quantities).
- if the errors are uncorrelated, the relative standard deviation of the ratio will be the square root of the sum of the squares of the individual relative standard deviations (again, in practice it's not that neat, but the relative standard deviation of the ratio is higher than the relative standard deviations of the individual quantities).

In chromatography, most people assume that the dominant source of uncorrelated errors is baseline noise, so looking at the relative error in the area ratio as a function of baseline noise may provide some insight into the relative contribution of the baseline correction algorithm.

Nice, thorough answer, Tom! I'm puzzled about units, though. S/N ratio has no unit. The ratio of two peak areas has no unit. Peak to peak noise does have a unit. If you try to express the ratio of two peak areas in terms of a peak-to-peak noise, the result will be an error with units. Is that appropriate?

You're thinking further forward than I was!

I was thinking of something like doing sufficient replicates to measure the RSD of the areas and the RSD of the ratios and then plotting those values as a function of the (square root of ???) the noise. It's not something I would do, but I was trying to second-guess the prof . . .

. . . Which is why pitfall should talk to his/her prof to get more information about the purpose behind the experiment.

agreed! You made more sense of the prof's aim than I could have. If in doubt, always ask the customer what they want...